Probabilistic Reasoning Research Articles

Data science with Vadalog: Knowledge Graphs with machine learning and reasoning in practice

Following the recent successful examples of large technology companies, many modern enterprises seek to build Knowledge Graphs to provide a unified view of corporate knowledge, and to draw deep insights using machine learning and logical reasoning. There is currently a perceived disconnect between the traditional approaches for data science, typically based on machine learning and statistical modeling, and systems for reasoning with domain knowledge. In this paper, we demonstrate how to perform a broad spectrum of data science tasks in a unified Knowledge Graph environment. This includes data wrangling, complex logical and probabilistic reasoning, and machine learning. We base our work on the state-of-the-art Knowledge Graph Management System Vadalog, which delivers highly expressive and efficient logical reasoning and provides seamless integration with modern data science toolkits such as the Jupyter platform. We argue that this is a significant step forward towards practical, holistic data science workflows that combine machine learning and reasoning in data science.

Prediction of future paths of mobile objects using path library

Abstract In situational awareness, the ability to make predictions about the near future situation in the area under surveillance is often as essential as being aware of the current situation. We introduce a privacy-preserving instance-based prediction method, where a path library is collected by learning earlier paths of mobile objects in the area of surveillance. The input to the prediction is the most recent coordinates of the objects in the scene. Based on similarity to short segments of currently tracked paths, a relative weight is associated with each path in the library. Future paths are predicted by computing the weighted average of the library paths. We demonstrate the operation of a situational awareness system where privacy-preserving data are extracted from an inexpensive computer vision which consists of a camera-equipped Raspberry PI-based edge device. The system runs a deep neural network-based object detection algorithm on the camera feed and stores the coordinates, object class labels, and timestamps of the detected objects. We used probabilistic reasoning based on joint probabilistic data association, Hungarian algorithm, and Kalman filter to infer which detections from different time instances came from the same object.

Novel Methods in the Surveillance of Influenza-Like Illness in Germany Using Data From a Symptom Assessment App (Ada): Observational Case Study.

BackgroundParticipatory epidemiology is an emerging field harnessing consumer data entries of symptoms. The free app Ada allows users to enter the symptoms they are experiencing and applies a probabilistic reasoning model to provide a list of possible causes for these symptoms.ObjectiveThe objective of our study is to explore the potential contribution of Ada data to syndromic surveillance by comparing symptoms of influenza-like illness (ILI) entered by Ada users in Germany with data from a national population-based reporting system called GrippeWeb.MethodsWe extracted data for all assessments performed by Ada users in Germany over 3 seasons (2017/18, 2018/19, and 2019/20) and identified those with ILI (report of fever with cough or sore throat). The weekly proportion of assessments in which ILI was reported was calculated (overall and stratified by age group), standardized for the German population, and compared with trends in ILI rates reported by GrippeWeb using time series graphs, scatterplots, and Pearson correlation coefficient.ResultsIn total, 2.1 million Ada assessments (for any symptoms) were included. Within seasons and across age groups, the Ada data broadly replicated trends in estimated weekly ILI rates when compared with GrippeWeb data (Pearson correlation—2017-18: r=0.86, 95% CI 0.76-0.92; P<.001; 2018-19: r=0.90, 95% CI 0.84-0.94; P<.001; 2019-20: r=0.64, 95% CI 0.44-0.78; P<.001). However, there were differences in the exact timing and nature of the epidemic curves between years.ConclusionsWith careful interpretation, Ada data could contribute to identifying broad ILI trends in countries without existing population-based monitoring systems or to the syndromic surveillance of symptoms not covered by existing systems.

A Probabilistic Semantics for Belief Logic

Belief logic is one of the most important branches of philosophical logic. The standard approach for characterizing belief is based on the so-called possible worlds model within which the problem of logical omniscience is considered a significant defect. We present an alternative semantics for belief logic based on a probabilistic model, which formalizes the so-called Lockean thesis in philosophical literature. The Lockean thesis states that a person believes a proposition whenever they see that the probability of the proposition has reached or exceeded a prespecified threshold. We give a complete deductive system for probabilistic belief logic as well as detailed comparisons to existing frameworks of belief logic.

An Asymptotic Analysis of Probabilistic Logic Programming, with Implications for Expressing Projective Families of Distributions

AbstractProbabilistic logic programming is a major part of statistical relational artificial intelligence, where approaches from logic and probability are brought together to reason about and learn from relational domains in a setting of uncertainty. However, the behaviour of statistical relational representations across variable domain sizes is complex, and scaling inference and learning to large domains remains a significant challenge. In recent years, connections have emerged between domain size dependence, lifted inference and learning from sampled subpopulations. The asymptotic behaviour of statistical relational representations has come under scrutiny, and projectivity was investigated as the strongest form of domain size dependence, in which query marginals are completely independent of the domain size. In this contribution we show that every probabilistic logic program under the distribution semantics is asymptotically equivalent to an acyclic probabilistic logic program consisting only of determinate clauses over probabilistic facts. We conclude that every probabilistic logic program inducing a projective family of distributions is in fact everywhere equivalent to a program from this fragment, and we investigate the consequences for the projective families of distributions expressible by probabilistic logic programs.

Predicting Physics Achievement of 11th - grade Students through Critical and Logical Thinking Skills

The purpose of this study was to measure the extent to which critical thinking skills and logical thinking skills predicted the achievement in physics of 11th - grade students in Gaza. To this end, (215) students participated in the study. California Critical Thinking Skills Test (CCTST) and Test of Logical Thinking (TOLT), were used as data collection tools in the study. Data were analyzed by multiple stepwise regression analysis. Results indicated that the students’ scores of probabilistic reasoning and proportional reasoning (as logical thinking skills), and inference (as critical thinking skill) were significant predictors of physics achievement scores, explaining (15.7%) of the variance of physics achievement scores. In addition, findings indicated that the best predictor was probabilistic reasoning, explaining (9.2 %) of the variance. The study recommended that a physics curriculum should involve thinking skills, which predict students’ achievement in physics.

The Model Counting Competition 2020

Many computational problems in modern society account to probabilistic reasoning, statistics, and combinatorics. A variety of these real-world questions can be solved by representing the question in (Boolean) formulas and associating the number of models of the formula directly with the answer to the question. Since there has been an increasing interest in practical problem solving for model counting over the past years, the Model Counting Competition was conceived in fall 2019. The competition aims to foster applications, identify new challenging benchmarks, and promote new solvers and improve established solvers for the model counting problem and versions thereof. We hope that the results can be a good indicator of the current feasibility of model counting and spark many new applications. In this article, we report on details of the Model Counting Competition 2020, about carrying out the competition, and the results. The competition encompassed three versions of the model counting problem, which we evaluated in separate tracks. The first track featured the model counting problem, which asks for the number of models of a given Boolean formula. On the second track, we challenged developers to submit programs that solve the weighted model counting problem. The last track was dedicated to projected model counting. In total, we received a surprising number of nine solvers in 34 versions from eight groups.

Probabilistic Interpolation Recoder for Energy-Error-Product Efficient DBNs With p-Bit Devices

In this article, a probabilistic interpolation recoder (PIR) circuit is developed for deep belief networks (DBNs) with probabilistic spin logic (p-bit)-based neurons. To verify the functionality and evaluate the performance of the PIRs, we have implemented a <inline-formula><tex-math notation="LaTeX">$784 \times 200 \times 10$</tex-math></inline-formula> DBN circuit in SPICE for a pattern recognition application using the MNIST dataset. The PIR circuits are leveraged in the last hidden layer to interpolate the probabilistic output of the neurons, which are representing different output classes, through sampling the p-bit's output values and then counting them in a defined sampling time window. The PIR circuit is proposed as an alternative for conventional interpolation methods which were based on using a resistor-capacitor tank to integrate each neuron's output, followed by an analog-to-digital converter to generate the digital output. The circuit simulation results of PIR circuit exhibit at least 54, 81, and 78 percent reductions in power, energy, and energy-error-product, respectively, compared to previous techniques, without using any of the area-consuming analog components in the interpolation circuit. In addition, PIR circuits provide an inherent single stuck-at fault tolerant feature to mitigate both transient and permanent faults at the circuit's output. Reliability properties of the PIR circuits for single stuck-at faults are shown to be enhanced relative to conventional interpolation without requiring hardware redundancy.

Neuro-Fuzzy: Artificial Neural Networks &amp; Fuzzy Logic

Abstract: Neuro Fuzzy is a hybrid system that combines Artificial Neural Networks with Fuzzy Logic. Provides a great deal of freedom when it comes to thinking. This phrase, on the other hand, is frequently used to describe a system that combines both approaches. There are two basic streams of neural network and fuzzy system study. Modelling several elements of the human brain (structure, reasoning, learning, perception, and so on) as well as artificial systems and data: pattern clustering and recognition, function approximation, system parameter estimate, and so on. In general, neural networks and fuzzy logic systems are parameterized nonlinear computing methods for numerical data processing (signals, images, stimuli). These algorithms can be integrated into dedicated hardware or implemented on a general-purpose computer. The network system acquires knowledge through a learning process. Internal parameters are used to store the learned information (weights). Keywords: Artificial Neural Networks (ANNs), Neural Networks (NNs), Fuzzy Logic (FL), Neuro-Fuzzy, Probability Reasoning, Soft Computing, Fuzzification, Defuzzification, Fuzzy Inference Systems, Membership Function.

A Brief Roadmap into Uncertain Knowledge Representation via Probabilistic Description Logics

Logic-based knowledge representation is one of the main building blocks of (logic-based) artificial intelligence. While most successful knowledge representation languages are based on classical logic, realistic intelligent applications need to handle uncertainty in an adequate manner. Over the years, many different languages for representing uncertain knowledge—often extensions of classical knowledge representation languages—have been proposed. We briefly present some of the defining properties of these languages as they pertain to the family of probabilistic description logics. This limited view is intended to help pave the way for the interested researcher to find the most adequate language for their needs, and potentially identify the remaining gaps.

Symbolic Variable Elimination for Discrete and Continuous Graphical Models

Probabilistic reasoning in the real-world often requires inference incontinuous variable graphical models, yet there are few methods for exact, closed-form inference when joint distributions are non-Gaussian. To address this inferential deficit, we introduce SVE -- a symbolic extension of the well-known variable elimination algorithm to perform exact inference in an expressive class of mixed discrete and continuous variable graphical models whose conditional probability functions can be well-approximated as piecewise combinations of polynomials with bounded support. Using this representation, we show that we can compute all of the SVE operations exactly and in closed-form, which crucially includes definite integration w.r.t. multivariate piecewise polynomial functions. To aid in the efficient computation and compact representation of this solution, we use an extended algebraic decision diagram (XADD) data structure that supports all SVE operations. We provide illustrative results for SVE on probabilistic inference queries inspired by robotics localization and tracking applications that mix various continuous distributions; this represents the first time a general closed-form exact solution has been proposed for this expressive class of discrete/continuous graphical models.

An Object-Based Bayesian Framework for Top-Down Visual Attention

We introduce a new task-independent framework to model top-down overt visual attention based on graph-ical models for probabilistic inference and reasoning. We describe a Dynamic Bayesian Network (DBN) that infers probability distributions over attended objects and spatial locations directly from observed data. Probabilistic inference in our model is performed over object-related functions which are fed from manual annotations of objects in video scenes or by state-of-the-art object detection models. Evaluating over ∼3 hours (appx. 315,000 eye fixations and 12,600 saccades) of observers playing 3 video games (time-scheduling, driving, and flight combat), we show that our approach is significantly more predictive of eye fixations compared to: 1) simpler classifier-based models also developed here that map a signature of a scene (multi-modal information from gist, bottom-up saliency, physical actions, and events) to eye positions, 2) 14 state-of-the-art bottom-up saliency models, and 3) brute-force algorithms such as mean eye position. Our results show that the proposed model is more effective in employing and reasoning over spatio-temporal visual data.

Syntactic Requirements for Well-defined Hybrid Probabilistic Logic Programs

Hybrid probabilistic logic programs can represent several scenarios thanks to the expressivity of Logic Programming extended with facts representing discrete and continuous distributions. The semantics for this type of programs is crucial since it ensures that a probability can be assigned to every query. Here, following one recent semantics proposal, we illustrate a concrete syntax, and we analyse the syntactic requirements needed to preserve the well-definedness.

A probabilistic approximate logic for neuro-symbolic learning and reasoning

As witnessed by recent advances in deep learning technologies, neural network models of very high complexity have been successfully applied in many data-rich domains. Challenges remain, however, if the amount of training data is severely limited, which is often the case due to the cost of acquiring such data or due to interest in systems that are constantly evolving thereby imposing natural limits on how much data can be collected. The core hypothesis explored in this paper is that data (to some degree) can be substituted by domain knowledge, not only addressing the limited data problem but also offering potential improvements in data-rich settings. For the representation of suitable domain theories, we propose Probabilistic Approximate Logic (PALO) to deal with the natural uncertainty associated with such representations and also to serve as a foundation for a new class of neuro-symbolic architectures, in which both neural and symbolic computations can be peacefully and synergistically integrated. Utilizing TensorFlow and Maude as neural and symbolic frameworks, respectively, we discuss our prototypical implementation of PALO in what we call the Logical Imagination Engine (LIME). By means of a small toy example, we convey a glimpse of its capabilities, but we also briefly discuss some real-world applications and how it may serve as a prototypical framework to explore a broader range of neuro-symbolic strategies in the future.

Probabilistic Thinking: A Principle-Based Concept Analysis in the Context of Uncertainty in Chronic Illness.

The Reconceptualized Uncertainty in Illness Theory (RUIT) includes the concept of "probabilistic thinking" intending to explain the positive reappraisal of uncertainty in chronic illness. However, the description of the concept is vague, thereby limiting the understanding of the theory. Thus, the aim was to develop a theoretical definition of probabilistic thinking in order to increase the explanatory value of RUIT. We conducted a principle-based concept analysis by means of a conceptually driven literature search. Methods consisted of database, dictionary, lexicon, and free web searching as well as citation tracking. We analyzed the concept in terms of (a) epistemology, (b) pragmatics, (c) logic, and (d) linguistics. The final data set included 27 publications, 14 of them from nursing. (a) Probabilistic thinking is a coping strategy to handle uncertainty. It involves a focus on either possibilities (in nursing) or probabilities (in other disciplines). (b) There is a lack of operationalization in nursing, though three measurements focusing the handling of probabilities are offered in psychology. (c) Nursing authors interpreting probabilistic thinking as accepted uncertainty lacked logical appropriateness, since probability negotiates uncertainty. (d) Probabilistic thinking is used synonymously with positive thinking and probabilistic reasoning. Nurses working with chronically ill patients should consider the findings for the application of RUIT. They should recognize whether uncertainty is perceived as a danger and encourage probabilistic thinking. Efforts are necessary to achieve a common language between nursing and other disciplines in order to avoid misunderstandings in clinical practice and research.

Guest Editorial for Special Issue on Coded Computing

Computing is the next frontier for information theory. Intellectually, the goal of coded computing has been of interest from the days of von Neumann and Shannon. von Neumann examined this issue in his 1956 paper “Probabilistic Logics and the Synthesis of Reliable Organisms From Unreliable Components,” which was in turn motivated intellectually by Shannon’s 1948 paper, and by the application of understanding reliability of seemingly noisy biological systems. While the original biological application remains ill-understood, the recent increasing use of decentralized and distributed computing architectures, as well as increasingly noisy technologies at a device level, have motivated a resurgence of interest in the problem.

Message Passing Algorithms for Semiring-Based and Valued Constraint Satisfaction Problems

Local consistency algorithms, like arc consistency (AC) algorithms, are polynomial-time algorithms that prune the search space of constraint satisfaction problems (CSPs). In this paper, we present connections between message passing algorithms and AC for semiring-based CSPs (SCSPs) and valued CSPs (VCSPs), two well-established frameworks that generalize CSPs. Message passing algorithms are well known distributed search algorithms for solving many combinatorial problems in artificial intelligence, probabilistic reasoning, and information theory. However, the relationship between message passing algorithms and SCSPs or VCSPs still remains understudied. Towards this end, we propose the best-O message passing (BOMP) algorithm for SCSPs and VCSPs. We prove that, unlike other standard message passing algorithms which are in general not guaranteed to converge, the BOMP algorithm guarantees convergence for SCSPs and specific subclasses of VCSPs. We also theoretically study the relationship between the BOMP algorithm and AC on SCSPs, and empirically study the quality of the solutions produced by the BOMP algorithm for VCSPs.

Optimizing Probabilities in Probabilistic Logic Programs

AbstractProbabilistic logic programming is an effective formalism for encoding problems characterized by uncertainty. Some of these problems may require the optimization of probability values subject to constraints among probability distributions of random variables. Here, we introduce a new class of probabilistic logic programs, namely probabilisticoptimizablelogic programs, and we provide an effective algorithm to find the best assignment to probabilities of random variables, such that a set of constraints is satisfied and an objective function is optimized.

Counterexample Generation for Probabilistic Model Checking Micro-Scale Cyber-Physical Systems.

Micro-scale Cyber-Physical Systems (MCPSs) can be automatically and formally estimated by probabilistic model checking, on the level of system model MDPs (Markov Decision Processes) against desired requirements in PCTL (Probabilistic Computation Tree Logic). The counterexamples in probabilistic model checking are witnesses of requirements violation, which can provide the meaningful information for debugging, control, and synthesis of MCPSs. Solving the smallest counterexample for probabilistic model checking MDP has been proven to be an NPC (Non-deterministic Polynomial complete) problem. Although some heuristic methods are designed for this, it is usually difficult to fix the heuristic functions. In this paper, the Genetic algorithm optimized with heuristic, i.e., the heuristic Genetic algorithm, is firstly proposed to generate a counterexample for the probabilistic model checking MDP model of MCPSs. The diagnostic subgraph serves as a compact counterexample, and diagnostic paths of MDP constitute an AND/OR tree for constructing a diagnostic subgraph. Indirect path coding of the Genetic algorithm is used to extend the search range of the state space, and a heuristic crossover operator is used to generate more effective diagnostic paths. A prototype tool based on the probabilistic model checker PAT is developed, and some cases (dynamic power management and some communication protocols) are used to illustrate its feasibility and efficiency.

Extended Hapicare: A telecare system with probabilistic diagnosis and self-adaptive treatment

The massive growth of the population with chronic diseases calls for a telecare system to enhance their quality of life and reduce their treatment costs. Most of the current solutions depend on reliable data, deterministic rules, or the similarity of patients, while studies have shown otherwise. To this end, in this paper, we have extended our previous work on the Hapicare framework to integrate probabilistic diagnosis and self-adaptive treatment. Our new framework enables sensors’ datastream analysis and online decision-making. Its ontology-based reasoning uses Systematized Nomenclature of Medicine - Clinical Terms (SNOMED-CT) ontology to add contextual information to the collected data. Moreover, probabilistic reasoning is applied for diagnosis and screening to manage the uncertainty and unreliability of data as well as the indeterministic medical rules. The treatment system is designed to be modifiable by the experts and automatically adaptable to patients’ needs. The probabilistic diagnosis performance has been evaluated based on two public datasets regarding symptoms and risk factors of two chronic diseases: chronic kidney disease and dermatologic disease. The results show that our solution outperforms a classical classifier specifically when more than 40% of the data are missing. The proposed framework is also validated using four scenarios. The evaluation results demonstrate the ability of the proposed framework to help patients and doctors diagnose and treat medical conditions and episodes.